Typical peak sidelobe level of binary sequences

Simon Litsyn, Alexander Shpunt

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

For a binary sequence Sn = {si}n i=1 ∈{±1}n, the peak sidelobe level (PSL) is defined as M(Sn) = max k=1,2,...., n-1 | ∑ i=1 n-k SiSi+k|. It is shown that the distribution of M(Sn) is strongly concentrated, and asymptotically almost surely, γ(Sn) = M(Sn)/√ n ln n ∈ [1, √ 2]. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known bounds due to Moon and Moser [8] claiming that the typical value γ(Sn) ∈ [o (1/√ ln n), 2], and settles to the affirmative a conjecture of Dmitriev and Jedwab [2] on the growth rate of the typical peak sidelobe.

Original languageEnglish
Title of host publicationProceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008
Pages1755-1757
Number of pages3
DOIs
StatePublished - 2008
Event2008 IEEE International Symposium on Information Theory, ISIT 2008 - Toronto, ON, Canada
Duration: 6 Jul 200811 Jul 2008

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8101

Conference

Conference2008 IEEE International Symposium on Information Theory, ISIT 2008
Country/TerritoryCanada
CityToronto, ON
Period6/07/0811/07/08

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